nLab Euclid



Life and work

Euclid (Εὐκλείδης) of Alexandria was the ancient author of the Elements, a treatise consisting of thirteen books covering plane and solid geometry, arithmetic (elementary number theory), and an early theory of real numbers. He is regarded as the preeminent organizer of the mathematics of the Hellenistic world, and his work exerted a decisive influence, through the centuries to come, on the understanding and cultural image of mathematics as a rigorous deductive discipline.

Euclid's rigour became a byword for mathematics (and specifically for geometry) until the 19th century, particularly in contrast to the slapdash approach of infinitesimal calculus. By the end of that century, however, mathematical rigour had progressed beyond Euclid, and David Hilbert had to reorganise the foundations of geometry to fill in some of Euclid's gaps.

There is little hard data on Euclid as a person; it seems to be generally agreed that he worked and taught at the library at Alexandria during the reign of Ptolemy I (circa 300 BC), having earlier received his training in mathematics from students of Plato at Plato’s Academy in Athens.

One could say that Euclid was the ancient version of Bourbaki, who quite consciously fancied and presented themselves as a modern-day Euclid, collecting and reorganizing the mathematics of the day in rigorous logical form. (The naming of Bourbaki’s magnum opus, the Elements of Mathematics, is of course no coincidence.) One notable stylistic difference: Euclid freely employed pictures as visual aids to the logical demonstrations in the Elements, whereas Bourbaki wrote in rather a puritanical spirit, sternly forbidding the use of pictorial representations, perhaps to avoid the kinds of errors that Hilbert patched in Euclid's work.

The Elements

(Include some words on the extent to which Euclid actually wrote this by himself, or collected treatises which were works of others, etc. Either on a separate page, or else here with a redirect.)

category: people

Last revised on June 6, 2013 at 00:04:12. See the history of this page for a list of all contributions to it.